Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a...

36
Logic Gates

TAGS:

Transcript of Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a...

Page 1: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Logic Gates

Page 2: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Transistors as Switches

VBB voltage controls whether the transistor conducts in a common base configuration.

Logic circuits can be built

Page 3: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

AND

In order for current to flow, both switches must be closed¤ Logic notation AB = C

(Sometimes AB = C)

A B C

0 0 0

0 1 0

1 0 0

1 1 1

Page 4: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

OR

Current flows if either switch is closed¤ Logic notation A + B = C

A B C

0 0 0

0 1 1

1 0 1

1 1 1

Page 5: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Properties of AND and OR

Commutation¤ A + B = B + A¤ A B = B A

Same as

Same as

Page 6: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Properties of AND and OR

Associative Property¤ A + (B + C) = (A + B) + C

¤ A (B C) = (A B) C

=

Page 7: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Properties of AND and OR

Distributive Property¤ A + B C = (A + B) (A + C)¤ A + B C

A B C Q

0 0 0 0

0 0 1 0

0 1 0 0

1 0 0 1

1 0 1 1

1 1 0 1

1 1 1 1

Page 8: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Distributive Property

(A + B) (A + C)

A B C Q

0 0 0 0

0 0 1 0

0 1 0 0

1 0 0 1

1 0 1 1

1 1 0 1

1 1 1 1

Page 9: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Binary Addition

A B S C(arry)

0 0 0 0

1 0 1 0

0 1 1 0

1 1 0 1

Notice that the carry results are the same as AND

C = A B

Page 10: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Inversion (NOT)

A Q

0 1

1 0Logic:

AQ

Page 11: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Exclusive OR (XOR)

Either A or B, but not both

This is sometimes called the inequality detector, because the result will be 0 when the inputs are the same and 1 when they are different.

The truth table is the same as for S on Binary Addition. S = A B

A B S

0 0 0

1 0 1

0 1 1

1 1 0

Page 12: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Getting the XOR

A B S

0 0 0

1 0 1

0 1 1

1 1 0

Two ways of getting S = 1

BAor BA

Page 13: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Circuit for XOR

Accumulating our results: Binary addition is the result of XOR plus AND

BA BABA

Page 14: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Half Adder

Called a half adder because we haven’t allowed for any carry bit on input. In elementary addition of numbers, we always need to allow for a carry from one column to the next.

18

25

4

3 (plus a carry)

Page 15: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Full Adder

INPUTS OUTPUTS

A B CIN COUT S

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Page 16: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Full Adder Circuit

Page 17: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Chaining the Full Adder

Possible to use the same scheme for subtraction by

noting that

A – B = A + (-B)

Page 18: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Binary CountingUse 1 for ON

Use 0 for OFF

= 00101011

Binary Counter

So our example has 25 + 23 + 21 + 20 = 32 + 8 + 2 + 1 = 43

http://www.frontiernet.net/~prof_tcarr/BinaryCounter.html
Page 19: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Counting in Binary

1 1 11 1011 21 10101

2 10 12 1100 22 10110

3 11 13 1101 23 10111

4 100 14 1110 24 11000

5 101 15 1111 25 11001

6 110 16 10000 26 11010

7 111 17 10001 27 11011

8 1000 18 10010 28 11100

9 1001 19 10011 29 11101

10 1010 20 10100 30 11110

Page 20: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

NAND (NOT AND)

A B Q

0 0 1

0 1 1

1 0 1

1 1 0

BAQ

Page 21: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

NOR (NOT OR)

A B Q

0 0 1

0 1 0

1 0 0

1 1 0

BAQ

Page 22: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Exclusive NOR

A B Q

0 0 1

0 1 0

1 0 0

1 1 1

Equality Detector

BAQ

Page 23: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Summary

Summary for all 2-input gates

Inputs Output of each gate

 A   B  AND NAND  OR  NOR XOR XNOR

0 0 0 1 0 1 0 1

0 1 0 1 1 0 1 0

1 0 0 1 1 0 1 0

1 1 1 0 1 0 0 1

Page 24: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Number Systems

Decimal (base 10) {0 1 2 3 4 5 6 7 8 9}¤ Place value gives a logarithmic representation

of the number¤ Ex. 4378 means

۞ 4 X 103 = 4000۞ 3 X 102 = 300۞ 7 X 101 = 70۞ 8 X 100 = 8

¤ The place also gives the exponent of the base

Page 25: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Example

432,600

4 3 2 6 0 0

105

104

103

100

101

102

Powers of ten:

100 = 1 102 = 100 104 = 10000

101 = 10 103 = 1000 105 = 100000

Page 26: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Binary (base 2) {0 1}Binary Decimal

0 0

1 1

10 2

11 3

100 4

101 5

110 6

111 7

1000 8

1001 9

1010 10

Page 27: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Example

1 1 0 1 1 0 0 1

27

26

25

20

21

22

24 23

Page 28: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Decimal Equivalent

1101 1001 1 X 27 = 128 + 1 X 26 = 64 + 0 X 25 = 0 + 1 X 24 = 16 + 1 X 23 = 8 + 0 X 22 = 0 + 0 X 21 = 0 + 1 X 20 = 1 217

Notice how powers of two stand out:

20 = 1

21 = 10

22 = 100

23 = 1000

Page 29: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Decimal to Binary Conversion

Ex. 575¤ Find the largest power of two less than the number

۞ 29 = 512

¤ Subtract that power of two from the number۞ 575 – 512 = 63

¤ Repeat steps 1 and 2 for the new result until you reach zero.۞ 25 = 32 63 – 32 = 31۞ 24 = 16 31 – 16 = 15۞ 23 = 8 15 – 8 = 7۞ 22 = 4 7 – 4 = 3۞ 21 = 2 3 – 2 = 1۞ 20 = 1 1 – 1 = 0

¤ Construct the number۞ 1000111111

Page 30: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Another Example

144¤ 27 = 128 144 – 128 = 16¤ 24 = 16 16 – 16 = 0

Result 10010000

Page 31: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Hexadecimal (base 16)

{0 1 2 3 4 5 6 7 8 9 A B C D E F} Assignments Dec Hex Dec Hex

0 0 8 8

1 1 9 9

2 2 10 A

3 3 11 B

4 4 12 C

5 5 13 D

6 6 14 E

7 7 15 F

Page 32: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Example

163

162

160

161

3 B 6 E

3 X 163 = 12288

11 X 162 = 2816

6 X 161 = 96

14 X 160 = 14

15214

Page 33: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Hexadecimal is Convenient for Binary Conversion

Binary Hex Binary Hex

0 0 1001 29

1 1 1010 A

10 2 1011 B

11 3 1100 C

100 4 1101 D

101 5 1110 E

110 6 1111 F

111 7 1 0000 10

1000 8 Nibble

Page 34: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Binary to Hex Conversion

Group binary number by fours (nibbles)¤ 1101 1001 0110

Convert each nibble into hex equivalent¤ 1101 1001 0110

D 9 6

Page 35: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Decimal to Hex Conversion

Ex. 284¤ 162 = 256 284 – 256 = 28¤ 161 = 16 28 - 16 = 12 (Hex C)

¤ Result 1 1 C

Page 36: Logic Gates. Transistors as Switches ¡V BB voltage controls whether the transistor conducts in a common base configuration. ¡Logic circuits can be built.

Another Example with an Extension

1054¤ 162 = 256

۞But we have several multiples of 256 in 1054– 1054/256 = 4.12 take integer part– This eliminates 4*256 = 1024

۞ 1054 – 1024 = 30

¤ 161 = 16 30 – 16 = 14 (Hex E)

¤ Result 4 1 E


A 45nm Logic Technology with High-k+Metal Gate Transistors ...

A 45nm Logic Technology with High-k+Metal Gate Transistors ...

Transistors as Digital Switches: Intro to Logic Gates Circuits that really count.

Transistors as Digital Switches: Intro to Logic Gates Circuits that really count.

TRANSISTORS WORK - Joe Knows Electronicswiki.joeknowselectronics.com/images/2/23/JoeKnows_HowTransistors… · Today, more NPN transistors are used ... association with digital logic

TRANSISTORS WORK - Joe Knows Electronicswiki.joeknowselectronics.com/images/2/23/JoeKnows_HowTransistors… · Today, more NPN transistors are used ... association with digital logic

Introduction to Computing Systems from bits & gates to C & beyond Chapter 3 Digital Logic Structures Transistors Logic gates & Boolean logic Combinational.

Introduction to Computing Systems from bits & gates to C & beyond Chapter 3 Digital Logic Structures Transistors Logic gates & Boolean logic Combinational.

Gates and Logic: From switches to Transistors , Logic Gates and Logic Circuits

Gates and Logic: From switches to Transistors , Logic Gates and Logic Circuits

Digital Logic: From Transistors to Gates - Course Web Pages · PDF fileDigital Logic: From Transistors to Gates. ... Switch-based circuits. can easily represent two states: ... CMPE12

Digital Logic: From Transistors to Gates - Course Web Pages · PDF fileDigital Logic: From Transistors to Gates. ... Switch-based circuits. can easily represent two states: ... CMPE12

Gates and Logic: From switches to Transistors, Logic Gates ... fileGoals for Today From Switches to Logic Gates to Logic Circuits Logic Gates • From switches • Truth Tables Logic

Gates and Logic: From switches to Transistors, Logic Gates ... fileGoals for Today From Switches to Logic Gates to Logic Circuits Logic Gates • From switches • Truth Tables Logic

Gates and Logic: From switches to Transistors, Logic Gates ... · PDF fileGates and Logic: From switches to Transistors, Logic Gates and Logic Circuits ... (ignoring inverters) minterm

Gates and Logic: From switches to Transistors, Logic Gates ... · PDF fileGates and Logic: From switches to Transistors, Logic Gates and Logic Circuits ... (ignoring inverters) minterm

Digital Electronics Part I Combinational and Sequential Logic · –Combinational logic circuits –Sequential logic circuits –How digital logic gates are built using transistors

Digital Electronics Part I Combinational and Sequential Logic · –Combinational logic circuits –Sequential logic circuits –How digital logic gates are built using transistors

W04 Transistors and Applications - DEUkisi.deu.edu.tr/aytac.goren/ELK2018/h4.pdf · W04 Transistors and Applications ... W10 Digital Logic Circuits (Gates and Flip Flops) ... Transistors

W04 Transistors and Applications - DEUkisi.deu.edu.tr/aytac.goren/ELK2018/h4.pdf · W04 Transistors and Applications ... W10 Digital Logic Circuits (Gates and Flip Flops) ... Transistors

Transistors, Boolean Logic and Logical Gates

Transistors, Boolean Logic and Logical Gates

Today's Goalskilyos.ee.bilkent.edu.tr/~eee314/downloads/l19.pdf · MOS transistors NMOS logic CMOS logic Transfer characteristics Power dissipation Delay Fan-out Logic design Logic

Today's Goalskilyos.ee.bilkent.edu.tr/~eee314/downloads/l19.pdf · MOS transistors NMOS logic CMOS logic Transfer characteristics Power dissipation Delay Fan-out Logic design Logic

Gates and Logic: From switches to Transistors, … and Logic: From switches to Transistors, Logic Gates and Logic Circuits Hakim Weatherspoon CS 3410, Spring 2013 Computer Science

Gates and Logic: From switches to Transistors, … and Logic: From switches to Transistors, Logic Gates and Logic Circuits Hakim Weatherspoon CS 3410, Spring 2013 Computer Science

CMOS Transistors and Boolean Logic Gates

CMOS Transistors and Boolean Logic Gates

Gates and Logic: From Transistors to Logic Gates and Logic ... · Building Functions: Logic Gates • NOT: • AND: • OR: • Logic Gates digital circuit that either allows a signal

Gates and Logic: From Transistors to Logic Gates and Logic ... · Building Functions: Logic Gates • NOT: • AND: • OR: • Logic Gates digital circuit that either allows a signal

Transistors and Logic

Transistors and Logic

Gates and Logic: From switches to Transistors - Cornell University

Gates and Logic: From switches to Transistors - Cornell University

Gates and Logic: From Transistors to Logic Gates and Logic ......Gates and Logic: From Transistors to Logic Gates and Logic Circuits [Weatherspoon, Bala, Bracy, and Sirer] Prof. Hakim

Gates and Logic: From Transistors to Logic Gates and Logic ......Gates and Logic: From Transistors to Logic Gates and Logic Circuits [Weatherspoon, Bala, Bracy, and Sirer] Prof. Hakim

Anatomy of a Mobile - eprg.org · Transistors • A CPU is a collection of transistors • All digital logic devices are built out of Transistors • 4 transistors will build a NAND

Anatomy of a Mobile - eprg.org · Transistors • A CPU is a collection of transistors • All digital logic devices are built out of Transistors • 4 transistors will build a NAND

Gates and Logic: From switches to Transistors, Logic Gates and Logic Circuits Hakim Weatherspoon CS 3410, Spring 2013 Computer Science Cornell University.

Gates and Logic: From switches to Transistors, Logic Gates and Logic Circuits Hakim Weatherspoon CS 3410, Spring 2013 Computer Science Cornell University.